An analysis of pulsation periods of long period variable stars

Summary. We report the results of a period change analysis of time series observations for 378 pulsating variable stars. The null hypothesis of no trend in expected periods is tested for each of the stars. The tests are non‐parametric in that potential trends are estimated by local linear smoothers. Our testing methodology has some novel features. First, the null distribution of a test statistic is defined to be the distribution that results in repeated sampling from a population of stars. This distribution is estimated by means of a bootstrap algorithm that resamples from the collection of 378 stars. Bootstrapping in this way obviates the problem that the conditional sampling distribution of a statistic, given a particular star, may depend on unknown parameters of that star. Another novel feature of our test statistics is that one‐sided cross‐validation is used to choose the smoothing parameters of the local linear estimators on which they are based. It is shown that doing so results in tests that are tremendously more powerful than analogous tests that are based on the usual version of cross‐validation. The positive false discovery rate method of Storey is used to account for the fact that we simultaneously test 378 hypotheses. We ultimately find that 56 of the 378 stars have changes in mean pulsation period that are significant when controlling the positive false discovery rate at the 5% level.